Humans and animals live in, and interact with, the 3D world around them. To understand humans then, we must understand the surfaces that support them and the objects with which they interact. To that end, we develop methods to estimate the structure and motion of the world from a single image, from video, or from multiple images. We approach this by combining unsupervised learning with physical knowlege of the world.

For moving scenes, we compute the optical flow representing the projection of the 3D motion field into the image. In doing so, we exploit the geometric structure of the problem to simplify it. If the scene is rigid and only the camera moves, then the optical flow is completely described by the depth of the scene and the camera motion. Real scenes, however, contain rigid structure and independently moving objects. To deal with this, we segment the scene into regions corresponding to the different types of motion. To do so we exploit different constraints that are both geometric and semantic.

In the latter case, we know that certain objects like animals and cars can move independently while others, like buildings, cannot. Additionally objects like the road are typically planar and hence their motion is simply modeled. Thus if we have a semantic segmentation of the scene, this gives us strong information about what motions may be present. We argue that segmentation and motion estimation go hand in hand and we have explored many methods to do both in a coupled way.

Our most recent work focuses on the unsupervised learning of motion, scene depth, camera motion, and segmentation. To do this we formulate a problem of competitive collaboration in which different neural networks vie to explain the motion in the scene. To make this work, the physical constraints about motion in rigid scenes are critical. This geometric information allows us to learn depth from a single image without supervision. Motion makes this possible because scene structure is constant over time, allowing motion over time to inform the network about scene depth.

This work demonstrates that classical physical and geometric constraints that we already know about the world and its motion are not only compatible with deep learning but can play a critical role in enabling unsupervised learning. In a sense, the physics of the world provide a form of pre-existing supervision.

Our ongoing work combines people, scenes, and unsupervised learning to derive coherent explanations of the 3D world. Specifically, we care about people, their motion, and their interactions with the scene. We think that coupling the estimation of human motion with 3D scene understanding will improve both.

34 results

2018

In German Conference on Pattern Recognition (GCPR), October 2018 (inproceedings)

Abstract

The difficulty of annotating training data is a major obstacle to using CNNs for low-level tasks in video. Synthetic data often does not generalize to real videos, while unsupervised methods require heuristic n losses. Proxy tasks can overcome these issues, and start by training a network for a task for which annotation is easier or which can be trained unsupervised. The trained network is then fine-tuned for the original task using small amounts of ground truth data. Here, we investigate frame interpolation
as a proxy task for optical flow. Using real movies, we train a CNN unsupervised for temporal interpolation. Such a network implicitly estimates motion, but cannot handle untextured regions. By fine-tuning on small amounts of ground truth flow, the network can learn to fill in homogeneous regions and compute full optical flow fields. Using this unsupervised pre-training, our network outperforms similar architectures that were trained supervised using synthetic optical flow.

The estimation of motion in video sequences establishes temporal correspondences between pixels and surfaces and allows reasoning about a scene using multiple frames. Despite being a focus of research for over three decades, computing motion, or optical flow, remains challenging due to a number of difficulties, including the treatment of motion discontinuities and occluded regions, and the integration of information from more than two frames. One reason for these issues is that most optical flow algorithms only reason about the motion of pixels on the image plane, while not taking the image formation pipeline or the 3D structure of the world into account. One approach to address this uses layered models, which represent the occlusion structure of a scene and provide an approximation to the geometry. The goal of this dissertation is to show ways to inject additional knowledge about the scene into layered methods, making them more robust, faster, and more accurate. First, this thesis demonstrates the modeling power of layers using the example of motion blur in videos, which is caused by fast motion relative to the exposure time of the camera. Layers segment the scene into regions that move coherently while preserving their occlusion relationships. The motion of each layer therefore directly determines its motion blur. At the same time, the layered model captures complex blur overlap effects at motion discontinuities. Using layers, we can thus formulate a generative model for blurred video sequences, and use this model to simultaneously deblur a video and compute accurate optical flow for highly dynamic scenes containing motion blur. Next, we consider the representation of the motion within layers. Since, in a layered model, important motion discontinuities are captured by the segmentation into layers, the flow within each layer varies smoothly and can be approximated using a low dimensional subspace. We show how this subspace can be learned from training data using principal component analysis (PCA), and that flow estimation using this subspace is computationally efficient. The combination of the layered model and the low-dimensional subspace gives the best of both worlds, sharp motion discontinuities from the layers and computational efficiency from the subspace. Lastly, we show how layered methods can be dramatically improved using simple semantics. Instead of treating all layers equally, a semantic segmentation divides the scene into its static parts and moving objects. Static parts of the scene constitute a large majority of what is shown in typical video sequences; yet, in such regions optical flow is fully constrained by the depth structure of the scene and the camera motion. After segmenting out moving objects, we consider only static regions, and explicitly reason about the structure of the scene and the camera motion, yielding much better optical flow estimates. Furthermore, computing the structure of the scene allows to better combine information from multiple frames, resulting in high accuracies even in occluded regions. For moving regions, we compute the flow using a generic optical flow method, and combine it with the flow computed for the static regions to obtain a full optical flow field. By combining layered models of the scene with reasoning about the dynamic behavior of the real, three-dimensional world, the methods presented herein push the envelope of optical flow computation in terms of robustness, speed, and accuracy, giving state-of-the-art results on benchmarks and pointing to important future research directions for the estimation of motion in natural scenes.

We address the unsupervised learning of several interconnected problems in low-level vision: single view depth prediction, camera motion estimation, optical flow and segmentation of a video into the static scene and moving regions. Our key insight is that these four fundamental vision problems are coupled and, consequently, learning to solve them together simplifies the problem because the solutions can reinforce each other by exploiting known geometric constraints. In order to model geometric constraints, we introduce Adversarial Collaboration, a framework that facilitates competition and collaboration between neural networks. We go beyond previous work by exploiting geometry more explicitly and segmenting the scene into static and moving regions. Adversarial Collaboration works much like expectation-maximization but with neural networks that act as adversaries, competing to explain pixels that correspond to static or moving regions, and as collaborators through a moderator that assigns pixels to be either static or independently moving. Our novel method integrates all these problems in a common framework and simultaneously reasons about the segmentation of the scene into moving objects and the static background, the camera motion, depth of the static scene structure, and the optical flow of moving objects. Our model is trained without any supervision and achieves state of the art results amongst unsupervised methods.

In this work, we propose a technique to convert CNN
models for semantic segmentation of static images into
CNNs for video data. We describe a warping method that
can be used to augment existing architectures with very lit-
tle extra computational cost. This module is called Net-
Warp and we demonstrate its use for a range of network
architectures. The main design principle is to use optical
flow of adjacent frames for warping internal network repre-
sentations across time. A key insight of this work is that fast
optical flow methods can be combined with many different
CNN architectures for improved performance and end-to-
end training. Experiments validate that the proposed ap-
proach incurs only little extra computational cost, while im-
proving performance, when video streams are available. We
achieve new state-of-the-art results on the standard CamVid
and Cityscapes benchmark datasets and show reliable im-
provements over different baseline networks. Our code and
models are available at http://segmentation.is.
tue.mpg.de

The optical flow of natural scenes is a combination of the motion of the observer and the independent motion of objects. Existing algorithms typically focus on either recovering motion and structure under the assumption of a purely static world or optical flow for general unconstrained scenes. We combine these approaches in an optical flow algorithm that estimates an explicit segmentation of moving objects from appearance and physical constraints. In static regions we take advantage of strong constraints to
jointly estimate the camera motion and the 3D structure of the scene over multiple frames. This allows us to also regularize the structure instead of the motion. Our formulation uses a Plane+Parallax framework, which works even under small baselines, and reduces the motion estimation to a one-dimensional search problem, resulting in more accurate estimation. In moving regions the flow is treated as unconstrained, and computed with an existing optical flow method. The resulting Mostly-Rigid Flow (MR-Flow) method achieves state-of-the-art results on both the MPISintel and KITTI-2015 benchmarks.

We learn to compute optical flow by combining a classical spatial-pyramid formulation with deep learning. This estimates large motions in a coarse-to-fine approach by warping one image of a pair at each pyramid level by the current flow estimate and computing an update to the flow. Instead of the standard minimization of an objective function at each pyramid level, we train one deep network per level to compute the flow update. Unlike the recent FlowNet approach, the networks do not need to deal with large motions; these are dealt with by the pyramid. This has several advantages. First, our Spatial Pyramid Network (SPyNet) is much simpler and 96% smaller than FlowNet in terms of model parameters. This makes it more efficient and appropriate for embedded applications. Second, since the flow at each pyramid level is small (< 1 pixel), a convolutional approach applied to pairs of warped images is appropriate. Third, unlike FlowNet, the learned convolution filters appear similar to classical spatio-temporal filters, giving insight into the method and how to improve it. Our results are more accurate than FlowNet on most standard benchmarks, suggesting a new direction of combining classical flow methods with deep learning.

Dense 3D reconstruction from RGB images is a highly ill-posed problem due to occlusions, textureless or reflective surfaces, as well as other challenges. We propose object-level shape priors to address these ambiguities. Towards this goal, we formulate a probabilistic model that integrates multi-view image evidence with 3D shape information from multiple objects. Inference in this model yields a dense 3D reconstruction of the scene as well as the existence and precise 3D pose of the objects in it. Our approach is able to recover fine details not captured in the input shapes while defaulting to the input models in occluded regions where image evidence is weak. Due to its probabilistic nature, the approach is able to cope with the approximate geometry of the 3D models as well as input shapes that are not present in the scene. We evaluate the approach quantitatively on several challenging indoor and outdoor datasets.

This paper introduces a fast and efficient segmentation technique for 2D images and 3D point clouds of building facades. Facades of buildings are highly structured and consequently most methods that have been proposed for this problem aim to make use of this strong prior information. Contrary to most prior work, we are describing a system that is almost domain independent and consists of standard segmentation methods. We train a sequence of boosted decision trees using auto-context features. This is learned using stacked generalization. We find that this technique performs better, or comparable with all previous published methods and present empirical results on all available 2D and 3D facade benchmark datasets. The proposed method is simple to implement, easy to extend, and very efficient at test-time inference.

In European Conference on Computer Vision (ECCV), Lecture Notes in Computer Science, Springer, October 2016 (inproceedings)

Abstract

In this paper we propose a CNN architecture for semantic image segmentation. We introduce a new “bilateral inception” module that can be inserted in existing CNN architectures and performs bilateral filtering, at multiple feature-scales, between superpixels in an image. The feature spaces for bilateral filtering and other parameters of the module are learned end-to-end using standard backpropagation techniques. The bilateral inception module addresses two issues that arise with general CNN segmentation architectures. First, this module propagates information between (super) pixels while respecting image edges, thus using the structured information of the problem for improved results. Second, the layer recovers a full resolution segmentation result from the lower resolution solution of a CNN. In the experiments, we modify several existing CNN architectures by inserting our inception modules between the last CNN (1 × 1 convolution) layers. Empirical results on three different datasets show reliable improvements not only in comparison to the baseline networks, but also in comparison to several dense-pixel prediction techniques such as CRFs, while being competitive in time.

In IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), June 2016 (inproceedings)

Abstract

Semantic annotations are vital for training models for object recognition, semantic segmentation or scene understanding. Unfortunately, pixelwise annotation of images at very large scale is labor-intensive and only little labeled data is available, particularly at instance level and for street scenes. In this paper, we propose to tackle this problem by lifting the semantic instance labeling task from 2D into 3D. Given reconstructions from stereo or laser data, we annotate static 3D scene elements with rough bounding primitives and develop a probabilistic model which transfers this information into the image domain. We leverage our method to obtain 2D labels for a novel suburban video dataset which we have collected, resulting in 400k semantic and instance image annotations. A comparison of our method to state-of-the-art label transfer baselines reveals that 3D information enables more efficient annotation while at the same time resulting in improved accuracy and time-coherent labels.

In IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), June 2016 (inproceedings)

Abstract

In this paper, we propose a non-local structured prior for volumetric multi-view 3D reconstruction. Towards this goal, we present a novel Markov random field model based on ray potentials in which assumptions about large 3D surface patches such as planarity or Manhattan world constraints can be efficiently encoded as probabilistic priors. We further derive an inference algorithm that reasons jointly about voxels, pixels and image segments, and estimates marginal distributions of appearance, occupancy, depth, normals and planarity. Key to tractable inference is a novel hybrid representation that spans both voxel and pixel space and that integrates non-local information from 2D image segmentations in a principled way. We compare our non-local prior to commonly employed local smoothness assumptions and a variety of state-of-the-art volumetric reconstruction baselines on challenging outdoor scenes with textureless and reflective surfaces. Our experiments indicate that regularizing over larger distances has the potential to resolve ambiguities where local regularizers fail.

In IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), June 2016 (inproceedings)

Abstract

Video object segmentation is challenging due to fast moving objects, deforming shapes, and cluttered backgrounds. Optical flow can be used to propagate an object segmentation over time but, unfortunately, flow is often inaccurate, particularly around object boundaries. Such boundaries are precisely where we want our segmentation to be accurate. To obtain accurate segmentation across time, we propose an efficient algorithm that considers video segmentation and optical flow estimation simultaneously. For video segmentation, we formulate a principled, multiscale, spatio-temporal objective function that uses optical flow to propagate information between frames. For optical flow estimation, particularly at object boundaries, we compute the flow independently in the segmented regions and recompose the results. We call the process object flow and demonstrate the effectiveness of jointly optimizing optical flow and video segmentation using an iterative scheme. Experiments on the SegTrack v2 and Youtube-Objects datasets show that the proposed algorithm performs favorably against the other state-of-the-art methods.

In IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), June 2016 (inproceedings)

Abstract

Occlusion boundaries contain rich perceptual information about the underlying scene structure. They also provide important cues in many visual perception tasks such as scene understanding, object recognition, and segmentation. In this paper, we improve occlusion boundary detection via enhanced exploration of contextual information (e.g., local structural boundary patterns, observations from surrounding regions, and temporal context), and in doing so develop a novel approach based on convolutional neural networks (CNNs) and conditional random fields (CRFs). Experimental results demonstrate that our detector significantly outperforms the state-of-the-art (e.g., improving the F-measure from 0.62 to 0.71 on the commonly used CMU benchmark). Last but not least, we empirically assess the roles of several important components of the proposed detector, so as to validate the rationale behind this approach.

Existing optical flow methods make generic, spatially homogeneous, assumptions about the spatial structure of the flow. In reality, optical flow varies across an image depending on object class.
Simply put, different objects move differently. Here we exploit recent advances in static semantic scene segmentation to segment the image into objects of different types. We define different models of image motion in these regions depending on the type of object. For example, we model the motion on roads with homographies, vegetation with spatially smooth flow, and independently moving objects like cars and planes with affine motion plus deviations. We then pose the flow estimation problem using a novel formulation of localized layers, which addresses limitations of traditional layered models for dealing with complex scene motion. Our semantic flow method achieves the lowest error of any published monocular method in the KITTI-2015 flow benchmark and produces qualitatively better flow and segmentation than recent top methods on a wide range of natural videos.

2015

In IEEE International Conference on Computer Vision (ICCV), pages: 3514-3522, December 2015 (inproceedings)

Abstract

We formulate the estimation of dense depth maps from video sequences as a problem of intrinsic image estimation. Our approach synergistically integrates the estimation of multiple intrinsic images including depth, albedo, shading, optical flow, and surface contours. We build upon an example-based framework for depth estimation that uses label transfer from a database of RGB and depth pairs. We combine this with a method that extracts consistent albedo and shading from video. In contrast to raw RGB values, albedo and shading provide a richer, more physical, foundation for depth transfer. Additionally we train a new contour detector to predict surface boundaries from albedo, shading, and pixel values and use this to improve the estimation of depth boundaries. We also integrate sparse structure from motion with our method to improve the metric accuracy of the estimated depth maps. We evaluate our Intrinsic Depth method quantitatively by estimating depth from videos in the NYU RGB-D and SUN3D datasets. We find that combining the estimation of multiple intrinsic images improves depth estimation relative to the baseline method.

We propose to look at large-displacement optical flow from a discrete point of view. Motivated by the observation that sub-pixel accuracy is easily obtained given pixel-accurate optical flow, we conjecture that computing the integral part is the hardest piece of the problem. Consequently, we formulate optical flow estimation as a discrete inference problem in a conditional random field, followed by sub-pixel refinement. Naive discretization of the 2D flow space, however, is intractable due to the resulting size of the label set. In this paper, we therefore investigate three different strategies, each able to reduce computation and memory demands by several orders of magnitude. Their combination allows us to estimate large-displacement optical flow both accurately and efficiently and demonstrates the potential of discrete optimization for optical flow. We obtain state-of-the-art performance on MPI Sintel and KITTI.

Inferring 3D objects and the layout of indoor scenes from a single RGB-D image captured with a Kinect camera is a challenging task. Towards this goal, we propose a high-order graphical model and jointly reason about the layout, objects and superpixels in the image. In contrast to existing holistic approaches, our model leverages detailed 3D geometry using inverse graphics and explicitly enforces occlusion and visibility constraints for respecting scene properties and projective geometry. We cast the task as MAP inference in a factor graph and solve it efficiently using message passing. We evaluate our method with respect to several baselines on the challenging NYUv2 indoor dataset using 21 object categories. Our experiments demonstrate that the proposed method is able to infer scenes with a large degree of clutter and occlusions.

In Proc. of the ISPRS Workshop on Image Sequence Analysis (ISA), 2015 (inproceedings)

Abstract

Three-dimensional reconstruction of dynamic scenes is an important prerequisite for applications like mobile robotics or autonomous driving. While much progress has been made in recent years, imaging conditions in natural outdoor environments are still very challenging for current reconstruction and recognition methods. In this paper, we propose a novel unified approach which reasons jointly about 3D scene flow as well as the pose, shape and motion of vehicles in the scene. Towards this goal, we incorporate a deformable CAD model into a slanted-plane conditional random field for scene flow estimation and enforce shape consistency between the rendered 3D models and the parameters of all superpixels in the image. The association of superpixels to objects is established by an index variable which implicitly enables model selection. We evaluate our approach on the challenging KITTI scene flow dataset in terms of object and scene flow estimation. Our results provide a prove of concept and demonstrate the usefulness of our method.

We address the elusive goal of estimating optical flow both accurately and efficiently by adopting a sparse-to-dense approach. Given a set of sparse matches, we regress to dense optical flow using a learned set of full-frame basis
flow fields. We learn the principal components of natural flow fields using flow computed from four Hollywood
movies. Optical flow fields are then compactly approximated as a weighted sum of the basis flow fields. Our
new PCA-Flow algorithm robustly estimates these weights from sparse feature matches. The method runs in under
300ms/frame on the MPI-Sintel dataset using a single CPU and is more accurate and significantly faster than popular
methods such as LDOF and Classic+NL. The results, however, are too smooth for some applications. Consequently,
we develop a novel sparse layered flow method in which each layer is represented by PCA-flow. Unlike existing layered
methods, estimation is fast because it uses only sparse matches. We combine information from different layers into
a dense flow field using an image-aware MRF. The resulting PCA-Layers method runs in 3.6s/frame, is significantly
more accurate than PCA-flow and achieves state-of-the-art performance in occluded regions on MPI-Sintel.

This paper proposes a novel model and dataset for 3D scene flow estimation with an application to autonomous driving. Taking advantage of the fact that outdoor scenes often decompose into a small number of independently moving objects, we represent each element in the scene by its rigid motion parameters and each superpixel by a 3D plane as well as an index to the corresponding object. This minimal representation increases robustness and leads to a discrete-continuous CRF where the data term decomposes into pairwise potentials between superpixels and objects. Moreover, our model intrinsically segments the scene into its constituting dynamic components. We demonstrate the performance of our model on existing benchmarks as well as a novel realistic dataset with scene flow ground truth. We obtain this dataset by annotating 400 dynamic scenes from the KITTI raw data collection using detailed 3D CAD models for all vehicles in motion. Our experiments also reveal novel challenges which can't be handled by existing methods.

Stereo techniques have witnessed tremendous progress over the last decades, yet some aspects of the problem still remain challenging today. Striking examples are reflecting and textureless surfaces which cannot easily be recovered using traditional local regularizers. In this paper, we therefore propose to regularize over larger distances using object-category specific disparity proposals (displets) which we sample using inverse graphics techniques based on a sparse disparity estimate and a semantic segmentation of the image. The proposed displets encode the fact that objects of certain categories are not arbitrarily shaped but typically exhibit regular structures. We integrate them as non-local regularizer for the challenging object class 'car' into a superpixel based CRF framework and demonstrate its benefits on the KITTI stereo evaluation.

Videos contain complex spatially-varying motion blur due to the combination of object motion, camera motion, and depth variation with finite shutter speeds. Existing methods to estimate optical flow, deblur the images, and segment the scene fail in such cases. In particular, boundaries between differently moving objects cause problems, because here the blurred images are a combination of the blurred appearances of multiple surfaces. We address this with a novel layered model of scenes in motion. From a motion-blurred video sequence, we jointly estimate the layer segmentation and each layer's appearance and motion. Since the blur is a function of the layer motion and segmentation, it is completely determined by our generative model. Given a video, we formulate the optimization problem as minimizing the pixel error between the blurred frames and images synthesized from the model, and solve it using gradient descent. We demonstrate our approach on synthetic and real sequences.

Large motions remain a challenge for current optical flow algorithms. Traditionally, large motions are addressed using multi-resolution representations like Gaussian pyramids. To deal with large displacements, many pyramid levels are needed and, if an object is small, it may be invisible at the highest levels. To address this we decompose images using a channel representation (CR) and replace the standard brightness constancy assumption with a descriptor constancy assumption. CRs can be seen as an over-segmentation of the scene into layers based on some image feature. If the appearance of a foreground object differs from the background then its descriptor will be different and they will be represented in different layers.We create a pyramid by smoothing these layers, without mixing foreground and background or losing small objects. Our method estimates more accurate flow than the baseline on the MPI-Sintel benchmark, especially for fast motions and near motion boundaries.

Intrinsic images such as albedo and shading are valuable for later stages of visual processing. Previous methods for extracting albedo and shading use either single images or images together with depth data. Instead, we define intrinsic video estimation as the problem of extracting temporally coherent albedo and shading from video alone. Our approach exploits the assumption that albedo is constant over time while shading changes slowly. Optical flow aids in the accurate estimation of intrinsic video by providing temporal continuity as well as putative surface boundaries. Additionally, we find that the estimated albedo sequence can be used to improve optical flow accuracy in sequences with changing illumination. The approach makes only weak assumptions about the scene and we show that it substantially outperforms existing single-frame intrinsic image methods. We evaluate this quantitatively on synthetic sequences as well on challenging natural sequences with complex geometry, motion, and illumination.

The accuracy of optical flow estimation algorithms has been improving steadily as evidenced by results on the Middlebury optical flow benchmark. The typical formulation, however, has changed little since the work of Horn and Schunck. We attempt to uncover what has made recent advances possible through a thorough analysis of how the objective function, the optimization method, and modern implementation practices influence accuracy. We discover that "classical'' flow formulations perform surprisingly well when combined with modern optimization and implementation techniques. One key implementation detail is the median filtering of intermediate flow fields during optimization. While this improves the robustness of classical methods it actually leads to higher energy solutions, meaning that these methods are not optimizing the original objective function. To understand the principles behind this phenomenon, we derive a new objective function that formalizes the median filtering heuristic. This objective function includes a non-local smoothness term that robustly integrates flow estimates over large spatial neighborhoods. By modifying this new term to include information about flow and image boundaries we develop a method that can better preserve motion details. To take advantage of the trend towards video in wide-screen format, we further introduce an asymmetric pyramid downsampling scheme that enables the estimation of longer range horizontal motions. The methods are evaluated on Middlebury, MPI Sintel, and KITTI datasets using the same parameter settings.

In this paper, we present a comprehensive survey of Markov Random Fields (MRFs) in computer vision and image understanding, with respect to the modeling, the inference and the learning. While MRFs were introduced into the computer vision field about two decades ago, they started to become a ubiquitous tool for solving visual perception problems around the turn of the millennium following the emergence of efficient inference methods. During the past decade, a variety of MRF models as well as inference and learning methods have been developed for addressing numerous low, mid and high-level vision problems. While most of the literature concerns pairwise MRFs, in recent years we have also witnessed significant progress in higher-order MRFs, which substantially enhances the expressiveness of graph-based models and expands the domain of solvable problems. This survey provides a compact and informative summary of the major literature in this research topic.

Layered models allow scene segmentation and motion estimation to be formulated together and to inform one another. Traditional layered motion methods, however, employ fairly weak models of scene structure, relying on locally connected Ising/Potts models which have limited ability to capture long-range correlations in natural scenes. To address this, we formulate a fully-connected layered model that enables global reasoning about the complicated segmentations of real objects. Optimization with fully-connected graphical models is challenging, and our inference algorithm leverages recent work on efficient mean field updates for fully-connected conditional random fields. These methods can be implemented efficiently using high-dimensional Gaussian filtering. We combine these ideas with a layered flow model, and find that the long-range connections greatly improve segmentation into figure-ground layers when compared with locally connected MRF models. Experiments on several benchmark datasets show that the method can recover fine structures and large occlusion regions, with good flow accuracy and much lower computational cost than previous locally-connected layered models.

Layered models provide a compelling approach for estimating image motion and segmenting moving scenes. Previous methods, however, have failed to capture the structure of complex scenes, provide precise object boundaries, effectively estimate the number of layers in a scene, or robustly determine the depth order of the layers. Furthermore, previous methods have focused on optical flow between pairs of frames rather than longer sequences. We show that image sequences with more frames are needed to resolve ambiguities in depth ordering at occlusion boundaries; temporal layer constancy makes this feasible. Our generative model of image sequences is rich but difficult to optimize with traditional gradient descent methods. We propose a novel discrete approximation of the continuous objective in terms of a sequence of depth-ordered MRFs and extend graph-cut optimization methods with new “moves” that make joint layer segmentation and motion estimation feasible. Our optimizer,
which mixes discrete and continuous optimization, automatically determines the number of layers and reasons
about their depth ordering. We demonstrate the value of layered models, our optimization strategy, and the use of
more than two frames on both the Middlebury optical flow benchmark and the MIT layer segmentation benchmark.

We address the challenging task of decoupling material properties from lighting properties given a single image. In the last two decades virtually all works have concentrated on exploiting edge information to address this problem. We take a different route by introducing a new prior on reflectance, that models reflectance values as being drawn from a sparse set of basis colors. This results in a Random Field model with global, latent variables (basis colors) and pixel-accurate output reflectance values. We show that without edge information high-quality results can be achieved, that are on par with methods exploiting this source of information. Finally, we are able to improve on state-of-the-art results by integrating edge information into our model. We believe that our new approach is an excellent starting point for future developments in this field.

This chapter introduces the concept of a Steerable Random Field (SRF). In contrast to traditional Markov random field (MRF) models in low-level vision, the random field potentials of a SRF are defined in terms of filter responses that are steered to the local image structure. This steering uses the structure tensor to obtain derivative responses that are either aligned with, or orthogonal to, the predominant local image structure. Analysis of the statistics of these steered filter responses in natural images leads to the model proposed here. Clique potentials are defined over steered filter responses using a Gaussian scale mixture model and are learned from training data. The SRF model connects random fields with anisotropic regularization and provides a statistical motivation for the latter. Steering the random field to the local image structure improves image denoising and inpainting performance compared with traditional pairwise MRFs.

Our goal is to understand the principles of Perception, Action and Learning in autonomous systems that successfully interact with complex environments and to use this understanding to design future systems